Projects
days until the end of spring semester.days until Snakes on a Plane.
Boxes unpacked
Math article project
Finished mathematical core of article. Next: Write analytical core of article.
Dummit and Foote, Abstract Algebra
Finished section 1.6 (86 to go)
Silverman and Tate, Rational Points on Elliptic Curves
FInished 2.5 (31 to go)
Conway, Functions of One Complex Variable I
Finished section 7.5 (27 to go)
Munkres, Topology
Finished section 21 (60 to go)
Royden, Real Analysis
Finished section 2.4 (97 to go)
Nonfiction book project
Todo list uptodate
Fiction book project
1443 out of 100,000 projected words written.
Top 100 novels of all time
Reading Ulysses
IMDB top 250 films
Tengoku to jigoku next in queue.
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Vito Prosciutto: Teaching community college math on the road to a PhD.
Monday, October 24, 2005
18:31A question for algebraic geometry types
Given two curves f(x,y)=0 and g(x,y)=0 in CP^{2}, if there are no common components, the number of points of intersection of the two curves (including multiplicity) is deg(f)deg(g)My intuitive sense is that at higher dimensions, instead of counting points, we count the degrees of the curves generated by the intersections. e.g., in three dimensions, the intersection of two planes will be a line (1*1=1), the intersection of a plane and a 2nd degree surface will be a 2nd degree curve or two lines. I suppose tangent points probably turn into nice surfaces once we look beyond R^{3} to C^{3}. But it seems sufficiently basic that surely someone has already mapped this out and proven it.